# Modelling of miscible liquids with the Korteweg stress

Ilya Kostin^{[1]}; Martine Marion; Rozenn Texier-Picard; Vitaly A. Volpert

- [1] Université de Saint-Etienne, Équipe d’Analyse Numérique, 23 rue Paul MICHELON, 42023 Saint-Etienne Cedex 02, France;

- Volume: 37, Issue: 5, page 741-753
- ISSN: 0764-583X

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topKostin, Ilya, et al. "Modelling of miscible liquids with the Korteweg stress." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.5 (2003): 741-753. <http://eudml.org/doc/245627>.

@article{Kostin2003,

abstract = {When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, they immediately diffuse in each other. However if the diffusion is sufficiently slow, large concentration gradients exist during some time. They can lead to the appearance of an “effective interfacial tension”. To study these phenomena we use the mathematical model consisting of the diffusion equation with convective terms and of the Navier-Stokes equations with the Korteweg stress. We prove the global existence and uniqueness of the solution for the associated initial-boundary value problem in a two-dimensional bounded domain. We study the longtime behavior of the solution and show that it converges to the uniform composition distribution with zero velocity field. We also present numerical simulations of miscible drops and show how transient interfacial phenomena can change their shape.},

affiliation = {Université de Saint-Etienne, Équipe d’Analyse Numérique, 23 rue Paul MICHELON, 42023 Saint-Etienne Cedex 02, France;},

author = {Kostin, Ilya, Marion, Martine, Texier-Picard, Rozenn, Volpert, Vitaly A.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {miscible liquids; Korteweg stress; drops},

language = {eng},

number = {5},

pages = {741-753},

publisher = {EDP-Sciences},

title = {Modelling of miscible liquids with the Korteweg stress},

url = {http://eudml.org/doc/245627},

volume = {37},

year = {2003},

}

TY - JOUR

AU - Kostin, Ilya

AU - Marion, Martine

AU - Texier-Picard, Rozenn

AU - Volpert, Vitaly A.

TI - Modelling of miscible liquids with the Korteweg stress

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2003

PB - EDP-Sciences

VL - 37

IS - 5

SP - 741

EP - 753

AB - When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, they immediately diffuse in each other. However if the diffusion is sufficiently slow, large concentration gradients exist during some time. They can lead to the appearance of an “effective interfacial tension”. To study these phenomena we use the mathematical model consisting of the diffusion equation with convective terms and of the Navier-Stokes equations with the Korteweg stress. We prove the global existence and uniqueness of the solution for the associated initial-boundary value problem in a two-dimensional bounded domain. We study the longtime behavior of the solution and show that it converges to the uniform composition distribution with zero velocity field. We also present numerical simulations of miscible drops and show how transient interfacial phenomena can change their shape.

LA - eng

KW - miscible liquids; Korteweg stress; drops

UR - http://eudml.org/doc/245627

ER -

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